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Paper   IPM / M / 8733
School of Mathematics
  Title:   The Skolem-Bang theorems in ordered fields with an IP
  Author(s):  S. M. Ayat
  Status:   To Appear
  Journal: J. Algebra
  Supported by:  IPM
  Abstract:
This paper is concerned with the extent to which the Skolem-Bang theorems in Diophantine approximations generalize from the standard setting of 〈\mathbbR , \mathbbZ〉 to structures of the form 〈F, I 〉, where F is an ordered field and I is an integer part of F. We show that some of these theorems are hold unconditionally in general case (ordered fields with an integer part). The remainder results are based on Dirichlet's and Kronecker's theorems. Finally we extend Dirichlet's theorem: to ordered fields with IE1 integer part.


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